Einar Iversen from NORSAR (Norway) visited us for 11 days, from 24 November 2003 to 4 December 2003. The mutual discussions were primarily devoted to the problems of seismic wave propagation in anisotropic structures and to the coupling ray theory. We discussed the isotropic and anisotropic common ray approximations and anisotropic-ray-theory ray as the reference frame for the coupling ray theory. Considerable attention has been devoted to parametrization and interpolation of the propagator matrix of the coupling equations for S waves, both in spatial and frequency domains, and to a possibility to define and apply the Hermitian 2x2 matrix of coupling-ray-theory travel times.